Question

At what temperature will the resistance of a copper wire become three times its value at $0^{\circ }C$ [Temperature coefficient of resistance for copper $=4\times {10}^{-3}pe{r}^{\circ }C$] :-

• A. ${400}^{\circ }C$
• B. ${450}^{\circ }C$
• C. ${500}^{\circ }C$
• D. ${550}^{\circ }C$

Answer 1

The correct option is C ${500}^{\circ }C$

As we know,

$R=R_0(1+\alpha \Delta T)$

give, $R=3R_0$ and $\alpha =4\times {10}^{-3}pe{r}^{0}C$

putting Values,

$3R_0=R_0(1+4\times {10}^{-3}(T_2-T_1\left)\right)$

$2=4\times {10}^{-3}(T_2-0)$ as $T_1=0^{0}C$

therefore,

$T_2={500}^{0}C$